I've done some spearfishing from Bahia Los Angeles through the Mulege/Bay of Conception area, and down past Loreto. I've always carried a couple machetes, knives, and an axe. I've never had any problems but, as noted above, that doesn't mean that you or I won't in the future. In Mexico you take your chances with a lot of things, including law enforcement. As in the US, if you are asked whether you have any "weapons", the answer is "no". Items of cutlery are tools.
One thing to warn your passengers about: When you are stopped at checkpoints and asked whether you have any guns, don't let anyone in the vehicle say "only spearguns." Some friends had a dive partner delayed for a couple hours over that one. Spearguns are better referred to as "fishing equipment" or just "spears".
It's a wonderful part of the world and I hope to spend more time down there. Have fun!